Systems and methods for  enhanced cellular automata algorithm for traffic flow modeling

ABSTRACT

An embodiment generally relates to systems and methods for enhanced cellular automata (CA) models. A processing module can generate a traffic model that comprises a set of vehicles. The traffic model can be processed according to the enhanced CA model. In particular, a perceived gap between vehicles in the set of vehicles can be identified. Further, a subsequent velocity of a following vehicle can be calculated based on metrics such as a maximum velocity, the perceived gap, and various time components.

FIELD OF THE INVENTION

This invention relates generally to traffic flow modeling and, moreparticularly, to systems and methods for an enhanced cellular automataalgorithm for traffic flow modeling.

BACKGROUND OF THE INVENTION

Traffic can be a major problem in some areas, such as in some urbaninfrastructures. In particular, the capacity of some road networks canbe at its limits, and frequent traffic jams or other congestions canimpact economic productivity and other factors. As a result of increasedurbanization, population density, motorization, and general population,traffic congestion has been increasing on transport infrastructures. Insome of these areas, the ability to construct more roads can beuntenable or impossible. Therefore, the efficient vehicular transport ofpeople and goods is vital to economies.

There is a need to accurately and realistically predict traffic flowpatterns within traffic infrastructures and networks. Further, becausemany urban areas are experiencing population growth, the need isexpanding. Various vehicle following models are presently used to modeltraffic flows and patterns. For example, existing modeling algorithmsinclude Chandler Model, Generalized GM Model, Gipps Model, Krauss Model,Leutzbach Model, Cellular Automata, Optimum Velocity Model, NewellModel, and others.

Some of the existing vehicle following modeling algorithms are dependenton a history of data. For example, when a vehicle switches lanes,history information can be “lost” and the results of some of theexisting models can be inaccurate or incomplete. In contrast, theCellular Automata (CA) model can be a useful model because it dependsonly on the previous step of the model. However, the CA model cansometimes prove, in some situations, to be inaccurate or otherwiseinsufficient.

Therefore, it may be desirable to have systems and methods for improvingthe performance and accuracy of traffic models. In particular, it may bedesirable to have systems and methods for modifying the CA modelingalgorithm to increase the accuracy and efficiency of traffic simulators.

SUMMARY

An embodiment pertains generally to a method of simulating traffic. Themethod comprises generating a traffic model comprising a leading vehicleand a following vehicle and identifying, in the traffic model, aperceived gap between the leading vehicle and the following vehicle.Further, the method comprises calculating, by a processor, a subsequentvelocity of the following vehicle at a subsequent time step based on amaximum velocity of the following vehicle, the perceived gap, and aspecified time parameter.

Another embodiment pertains generally to a system for simulatingtraffic. The system comprises a processor coupled to memory andconfigured to generate a traffic model comprising a leading vehicle anda following vehicle and identify, in the traffic model, a perceived gapbetween the leading vehicle and the following vehicle. Further, theprocessor is configured to calculate a subsequent velocity of thefollowing vehicle at a subsequent time step based on a maximum velocityof the following vehicle, the perceived gap, and a specified timeparameter.

BRIEF DESCRIPTION OF THE DRAWINGS

Various features of the embodiments can be more fully appreciated, asthe same become better understood with reference to the followingdetailed description of the embodiments when considered in connectionwith the accompanying figures, in which:

FIG. 1 illustrates an exemplary vehicle positioning environment inaccordance with embodiments;

FIG. 2 is a chart depicting traffic flow modeling data in accordancewith embodiments;

FIG. 3 is a chart depicting traffic flow modeling data in accordancewith embodiments;

FIG. 4 is a chart depicting traffic flow modeling data in accordancewith embodiments;

FIG. 5 illustrates an exemplary flow diagram of a traffic simulator inaccordance with embodiments;

FIG. 6 illustrates a hardware diagram in accordance with embodiments.

DESCRIPTIONOF THE EMBODIMENTS

Reference will now be made in detail to the present embodiments(exemplary embodiments) of the invention, examples of which areillustrated in the accompanying drawings. Wherever possible, the samereference numbers will be used throughout the drawings to refer to thesame or like parts. In the following description, reference is made tothe accompanying drawings that form a part thereof, and in which isshown by way of illustration specific exemplary embodiments in which theinvention may be practiced. These embodiments are described insufficient detail to enable those skilled in the art to practice theinvention and it is to be understood that other embodiments may beutilized and that changes may be made without departing from the scopeof the invention. The following description is, therefore, merelyexemplary.

While the invention has been illustrated with respect to one or moreimplementations, alterations and/or modifications can be made to theillustrated examples without departing from the spirit and scope of theappended claims. In addition, while a particular feature of theinvention may have been disclosed with respect to only one of severalimplementations, such feature may be combined with one or more otherfeatures of the other implementations as may be desired and advantageousfor any given or particular function. Furthermore, to the extent thatthe terms “including”, “includes”, “having”, “has”, “with”, or variantsthereof are used in either the detailed description and the claims, suchterms are intended to be inclusive in a manner similar to the term“comprising.” The term “at least one of” is used to mean one or more ofthe listed items can be selected.

Notwithstanding that the numerical ranges and parameters setting forththe broad scope of the invention are approximations, the numericalvalues set forth in the specific examples are reported as precisely aspossible. Any numerical value, however, inherently contains certainerrors necessarily resulting from the standard deviation found in theirrespective testing measurements. Moreover, all ranges disclosed hereinare to be understood to encompass any and all sub-ranges subsumedtherein. For example, a range of “less than 10” can include any and allsub-ranges between (and including) the minimum value of zero and themaximum value of 10, that is, any and all sub-ranges having a minimumvalue of equal to or greater than zero and a maximum value of equal toor less than 10, e.g., 1 to 5. In certain cases, the numerical values asstated for the parameter can take on negative values. In this case, theexample value of range stated as “less than 10” can assume values asdefined earlier plus negative values, e.g. -1, −1.2, −1.89, −2, −2.5,−3, −10, −20, −30, etc.

As used herein, “optimize” or variations thereof can be a general termthat can refer to the best available option. In other words, an“optimized” configuration need not represent the best possibleconfiguration, but instead can mean the preferred configuration of thepossible configurations. Further, the term “optimize” can also meanmaximize, enhance, improve, or other terms related to a preferred orimproved performance level.

As used herein, a “model” or variations thereof can be a generalizedterm that can refer to a simulation, forecast, abstraction, and/or thelike of data. A processing module, application, or other entity can usemodeling or variations thereof to process inputs or other available datato simulate one or more exemplary or real life environments. Forexample, according to the present embodiments, a traffic flow model canbe created and/or processed to simulate traffic flow in a roadwayinfrastructure. Further, as used herein, “traffic flow” or variationsthereof can refer to the movement of vehicles, such as automobiles,trucks, motorcycles, and the like, across or through roadways,intersections, highways, or any other infrastructure components.

Embodiments generally relate to systems and methods for modeling vehicletraffic flow. More particularly, a processing module, application, orother entity or logic can process and/or model traffic in accordancewith the techniques as described herein. In embodiments, the processingmodule can utilize Cellular Automata (CA) models and/or algorithms toforecast, simulate, or otherwise model traffic flow behavior. Theprocessing module can be a part of or otherwise incorporated into acomputing system, device, or other hardware.

In general, CA models and/or algorithms are discrete models that consistof a regular grid of “cells,” each of which is in a finite number ofstates. The cells evolve through a number of discrete time stepsaccording to a set of rules based on states (e.g. “on” and “off”) of aset of neighboring cells. The neighborhood of a specified cell can bedefined relative to the specified cell. For example, the neighborhood ofcells can be defined to be the set of cells a distance of two (2) orless from the specified cell. The initial time state can be t=0. Ageneration is created after a set of rules is tested and/or applied, andthe time state can be advanced to t=1, and so on. For example, a rulecan be that a specified cell is “on” in the next generation if three ormore of the cells in the neighborhood of the specified cell are “on,”otherwise the specified cell is “off” in the next generation. Inembodiments, the rules can be uniform for each cell in the grid, and canremain the same in subsequent generations. However, it should beunderstood that there can be multiple rules that can be applied tomultiple generations.

In general, CA models can capture micro-level data and/or dynamics, andapply those to traffic flow behavior on a macro level. For example,micro-level data can correspond to simulations of single vehicle-driverunits, and can comprise properties such as the position and velocity ofa single vehicle. In contrast, macro-level data can correspond tosimulations of multiple vehicles, and can comprise parameters such astravel time and throughput. CA models can capture complexities of realtraffic by allowing different vehicles to possess different behaviorssuch as, for example, lane change rules, reaction times,acceleration/deceleration, and other behaviors. As such, CA models canreproduce some non-trivial traffic phenomena such as, for example,spontaneous traffic jams.

Table 1 comprises notations, variables, and other data related to theembodiments as described herein. In particular, the symbols in the leftcolumn of Table 1 can refer to the variable notation corresponding tothe variable name in the middle column of Table 1. Further, the units ofthe corresponding variable are listed in the right column of Table 1.

TABLE 1 a_(n) Acceleration, vehicle n [m/s²] x_(n) Position, vehicle n[m] v_(n) Speed, vehicle n [m/s] Δx x_(n−1) − x_(n), space headway [m]Δv v_(n) − v_(n−1), difference in [m/s] speed v_(n) ^(desired) Desiredspeed, vehicle n [m/s] L_(n−1) Length, vehicle (n−1) [m] S_(n−1)Effective length (L_(n−1) + min [m] gap between stationary vehicles),vehicle (n-1) T Reaction time [s] Δt Units of time [s]

FIG. 1 is an illustration detailing an exemplary vehicle positioningenvironment 100. It should be readily apparent to one of ordinary skillin the art that the environment 100 depicted in FIG. 1 represents ageneralized schematic illustration and that other components can beadded or existing components can be removed or modified.

As shown in FIG. 1, the environment 100 can comprise a first vehicle (n)105 and a second vehicle (n-1) 110. The first vehicle 105 and the secondvehicle 110 can be traveling in a direction as indicated by 102, atrespective velocities of v_(n) and v_(n-1). As shown in FIG. 1, thex_(n) metric can correspond to the position of the first vehicle 105,and the x_(n-1) metric can correspond to the position of the secondvehicle. Further, the L_(n) metric can correspond to the length of thefirst vehicle 105 and the L_(n-1) metric can correspond to the length ofthe second vehicle 110. Moreover, the Δx metric can correspond to thespace headway between the first vehicle 105 and the second vehicle 110.

In embodiments, CA models can use variables to describe the dynamicproperties of traffic flow. The roads on which the vehicles travel canbe divided into sections of a certain length and the time can besegmented into steps of Δt. In embodiments, Δt can be approximatelyequal to the average reaction time of a human driver, such as, forexample, 1 second.

In embodiments, a CA model can be defined by equation.1:

$\begin{matrix}{{v_{n}\left( {t + {\Delta \; t}} \right)} = {\min \left\{ {\frac{g_{n}(t)}{T},{{v_{n}(t)} + a},V} \right\}}} & (1)\end{matrix}$

In equation 1, a corresponds to the maximum velocity change in each timestep. Further, g_(n) is the perceived gap or distance between vehicles,such as the perceived gap between a leading vehicle and a followingvehicle, wherein g_(n)(t)=x_(n-1)(t)−x_(n)(t)−s_(n-1). Moreparticularly, x_(n-1)(t) can correspond to the position of the leadingvehicle at time t and x_(n)(t) can correspond to the position of thefollowing vehicle at time t. In embodiments, the leading vehicle can bemoving or stationary. Still further, V is the maximum velocity of avehicle, T is an input parameter specified in a unit of time such as,for example, seconds, and Δt is the simulation time step or interval.

The CA model as defined by equation 1 can have some drawbacks, however.In particular, the drawbacks can occur when the following vehicle isgetting into a distance that is considered to be “close” to the leadingvehicle, especially in situations in which the leading vehicle isstationary. In embodiments, a distance that is considered to be “close”can be approximately 60 m, or other values. In these situations, thevelocity of the following vehicle, as modeled by equation (1), canchange suddenly, which leads to a “jump” in the acceleration of thefollowing vehicle. Further, when the velocity of the following vehiclereduces, the reduction can be sudden, thus impacting the deceleration ofthe following vehicle.

According to present embodiments, the CA model as defined in equation(1) can be optimized or otherwise enhanced such that the drawbacks ofthe CA model as defined in equation (1) can be reduced or eliminated.Further, the enhanced technique retains the advantage of the CA modelwhile correcting the velocity and acceleration drawbacks. The enhancedCA model can be defined by equation (2):

$\begin{matrix}{{v_{n}\left( {t + {\Delta \; t}} \right)} = {\min \left\{ {\sqrt{\frac{{Vg}_{n}(t)}{T^{*}}},{{v_{n}(t)} + a},V} \right\}}} & (2)\end{matrix}$

In equation (2), T′ is an input parameter specified in a unit of time(e.g. seconds), and is similar to T in equation (1), and the otherparameters correspond to the same variables or values as discussedherein. According to the enhanced CA model as defined in equation (2),the following vehicle will keep away from the leading vehicle a distancethat corresponds to the distance that the following vehicle will travelin a specified time (T′) with the following vehicle's next stepvelocity.

FIGS. 2-4 summarize the following vehicle's behavior when the leadingvehicle is stationary or stopped. There are a total of three (3) modelsor techniques depicted in FIGS. 2-4, namely, Gipps' safe distancealgorithm, the CA model as defined in equation (1), and the enhanced CAmodel as defined in equation (2).

FIG. 2 depicts a chart of the following vehicle's perceived gap (m) fromthe stopped leading vehicle as a function of time (s). Further, FIG. 3depicts a chart of the following vehicle's velocity (m/s) as a functionof perceived gap (m) when the leading vehicle is stopped. Still further,FIG. 4 depicts a chart of the following vehicle's velocity (m/s) as afunction of time (s) when the leading vehicle is stopped.

As shown in FIG. 2, the perceived gap (g_(n)) when the leading vehicleis stopped does not vary much among the three models. However, when thefollowing vehicle's velocity (v_(n)) is compared to the perceived gap,as shown in FIG. 3, the CA model as defined in equation (1) shows thatthe following vehicle's velocity increases in a linear fashion as theperceived gap increases, but then abruptly levels off when . theperceived gap hits about 60 meters. Because an abrupt leveling-off of avehicle's velocity is not common in reality, the CA model as defined inequation (1) can be inaccurate.

In contrast, in the enhanced CA model as defined in equation (2), and asshown in FIG. 3, the following vehicle's velocity increases more atsmall perceived gaps, and then gradually increases for all of the valuesof the perceived gaps. Therefore, the enhanced CA model as defined inequation (2) more accurately depicts the real-life behavior of thefollowing vehicle when the leading vehicle is stopped.

Further, as shown in FIG. 4, in the CA model as defined in equation (1),the following vehicle's velocity abruptly slows from a consistent speedwhen the time reaches about 2 seconds. This behavior, too, is not commonin reality, and the CA model as defined in equation (1) can further beinaccurate. In contrast, as shown in FIG. 4, in the enhanced CA model asdefined in equation (2), the following vehicle's velocity graduallydecreases as time progresses until the following vehicle's velocityreaches zero. This behavior is more accurate to a following vehicle'sactions in reality, and thus makes the enhanced CA model as defined inequation (2) a more accurate model than the CA model as defined inequation (1).

Referring to FIG. 5, depicted is a flowchart detailing a technique 500used to model traffic flow in accordance with the enhanced CA model asdefined in equation (2). It should be readily apparent to those ofordinary skill in the art that the flow diagram depicted in FIG. 5represents a generalized illustration and that other steps can be addedor existing steps can be removed or modified.

In 505, processing can begin. In 510, a traffic model can be generated.In embodiments, the traffic model can comprise a following vehicle, aleading vehicle positioned in front of the following vehicle, and/orother vehicles. In 515, a perceived gap between the leading vehicle andthe following vehicle can be identified. In embodiments, the perceivedgap can be calculated using an equation: x_(n-1)(t)−x_(n)(t)−s_(n-1),wherein x_(n-1)(t) corresponds to a position of the leading vehicle,x_(n)(t) corresponds to a position of the following vehicle, and s_(n-1)corresponds to a length of the leading vehicle. In further embodiments,the leading vehicle can be stationary.

In 520, a subsequent velocity of the following vehicle at a subsequenttime can be calculated based on a maximum velocity of the followingvehicle, the perceived gap, and a specified time. In embodiments, themaximum velocity can be an input parameter or can otherwise be availableto a processing module, application, or other logic. In embodiments, thesubsequent velocity can be calculated using an equation:

$\sqrt{\frac{{Vg}_{n}(t)}{T^{*}}},$

wherein V corresponds to the maximum velocity, g_(n)(t) corresponds tothe perceived gap, and T′ corresponds to the specified time. Further, inembodiments, the processing module can calculate a current velocity ofthe following vehicle at a current time, and select, as an output, aminimum of a set

$\left\{ {\sqrt{\frac{{Vg}_{n}(t)}{T^{*}}},{{v_{n}(t)} + a},V} \right\},$

wherein V corresponds to the maximum velocity g_(n)(t) corresponds tothe perceived gap, T′ corresponds to the specified time, v_(n)(t)corresponds to the current velocity, and a corresponds to a maximumallowable velocity change in one simulation time step.

After the subsequent velocities for any or all vehicles in the roadnetwork are calculated, processing can proceed back to 515 where a timesegment can be iterated and a new perceived gap can be calculated, inaddition to a new subsequent velocity. In embodiments, the processingcan repeat steps 515 and 520 one or more times, for a set time period, aset number of times, or any other repeat processing. In 525, a data setcan be generated based on the calculations. In embodiments, the data setcan comprise each identified or calculated perceived gap, subsequentvelocity, selected output in accordance with the enhanced CA model asdefined in equation (2), or other data. In 530, the data set can beprocessed to simulate a traffic flow within the traffic model. Inembodiments, the data set can be provided to a user, administrator, orother entity, for viewing, analysis, or other purposes, or can be storedin storage or memory for later retrieval.

FIG. 6 illustrates an exemplary diagram of hardware and other resourcesthat can be incorporated with processing and logic associated with thepresent embodiments. As shown in FIG. 6, a server 610 can be configuredto communicate with a network 609. In embodiments as shown, the server610 can comprise a processor 608 communicating with memory 602, such. aselectronic random access memory, or other forms of transitory ornon-transitory computer readable storage mediums, operating undercontrol of or in conjunction with an operating system 606. The operatingsystem 606 can be any commercial, open-source, or proprietary operatingsystem or platform. The processor 608 can communicate with a database615, such as a database stored on a local hard drive. While illustratedas a local database in the server 610, the database 615 can be separatefrom the server 610.

The processor 608 can further communicate with a network interface 604,such as an Ethernet or wireless data connection, which in turncommunicates with the network 609, such as the Internet or other publicor private networks. The processor 608 can also communicate with thedatabase 615 or any applications 605, such as applications associatedwith the processing module, to execute control logic and perform dataprocessing, as described herein.

While FIG. 6 illustrates the server 610 as a standalone systemcomprising a combination of hardware and software, the server 610 canalso be implemented as a software application or program capable ofbeing executed by a conventional computer platform. For example, itshould be understood that the components of the server 610 can beimplemented on user PCs or other hardware such that the user PCs cancommunicate directly with the database 615. Likewise, the server 610 canalso be implemented as a software module or program module capable ofbeing incorporated in other software applications and programs. Ineither case, the server 610 can be implemented in any type ofconventional proprietary or open-source computer language.

Certain embodiments can be performed as a computer program. The computerprogram can exist in a variety of forms both active and inactive. Forexample, the computer program can exist as software program(s) comprisedof program instructions in source code, object code, executable code orother formats; firmware program(s); or hardware description language(HDL) files. Any of the above can be embodied on a transitory ornon-transitory computer readable medium, which include storage devicesand signals, in compressed or uncompressed form. Exemplary computerreadable storage devices include conventional computer system RAM(random access memory), ROM (read-only memory), EPROM (erasable,programmable ROM), EEPROM (electrically erasable, programmable ROM), andmagnetic or optical disks or tapes. Exemplary computer readable signals,whether modulated using a carrier or. not, are signals that a computersystem hosting or running the present invention can be configured toaccess, including signals downloaded through the Internet or othernetworks. Concrete examples of the foregoing include distribution ofexecutable software program(s) of the computer program on a CD-ROM orvia Internet download. In a sense, the Internet itself, as an abstractentity, is a computer readable medium. The same is true of computernetworks in general.

While the invention has been described with reference to the exemplaryembodiments thereof, those skilled in the art will be able to makevarious modifications to the described embodiments without departingfrom the true spirit and scope. The terms and descriptions used hereinare set forth by way of illustration only and are not meant aslimitations. In particular, although the method has been described byexamples, the steps of the method can be performed in a different orderthan illustrated or simultaneously. Those skilled in the art willrecognize that these and other variations are possible within the spiritand scope as defined in the following claims and their equivalents.

1. A method of simulating traffic, the method comprising: generating atraffic model comprising a leading vehicle and a following vehicle;identifying, in the traffic model, a perceived gap between the leadingvehicle and the following vehicle; and calculating, by a processor, asubsequent velocity of the following vehicle at a subsequent time stepbased on a maximum velocity of the following vehicle, the perceived gap,and a specified time parameter.
 2. The method of claim 1, wherein thesubsequent velocity of the following vehicle is calculated using anequation $\sqrt{\frac{{Vg}_{n}(t)}{T^{*}}},$ wherein V corresponds tothe maximum velocity, g_(n)(t) corresponds to the perceived gap, and T′corresponds to the specified time parameter.
 3. The method of claim 1,wherein the perceived gap is calculated using an equationx_(n-1)(t)−x_(n)(t) −s_(n-1), wherein x_(n-1)(t) corresponds to aposition of the leading vehicle, x_(n)(t) corresponds to a position ofthe following vehicle, and s_(n-1) corresponds to a length of theleading vehicle.
 4. The method of claim 1, further comprising:calculating a current velocity of the following vehicle at a currenttime; and selecting, as an output, a minimum of a set$\left\{ {\sqrt{\frac{{Vg}_{n}(t)}{T^{*}}},{{v_{n}(t)} + a},V} \right\},$wherein V corresponds to the maximum velocity, g_(n)(t) corresponds tothe perceived gap, T′ corresponds to the specified time parameter,v_(n)(t) corresponds to the current velocity, and a corresponds to anallowable maximum velocity change in a single time step.
 5. The methodof claim 4, further comprising: providing the output to a user.
 6. Themethod of claim 1, further comprising: identifying at least oneadditional vehicle in the traffic model ; repeating the identifying andthe calculating for the at least one additional vehicle; and generatinga data set based on the repeating.
 7. The method of claim 1, furthercomprising: iterating a time step; repeating the identifying and thecalculating according to the time step; and generating a data set basedon the repeating.
 8. The method of claim 7, further comprising:processing the data set to simulate a traffic flow within the trafficmodel.
 9. The method of claim 7, further comprising: storing the dataset in memory.
 10. The method of claim 1, wherein the leading vehicle isstationary.
 11. The method of claim 1, wherein the traffic model is usedto model a traffic flow in a transportation infrastructure.
 12. A systemfor simulating traffic, the system comprising: a processor coupled tomemory and configured to perform actions comprising: generating atraffic model comprising a leading vehicle and a following vehicle;identifying, in the traffic model, a perceived gap between the leadingvehicle and the following vehicle; and calculating a subsequent velocityof the following vehicle at a subsequent time step based on a maximumvelocity of the following vehicle, the perceived gap, and a specifiedtime parameter.
 13. The system of claim 12, wherein the subsequentvelocity of the following vehicle is calculated using an equation$\sqrt{\frac{{Vg}_{n}(t)}{T^{*}}},$ wherein V corresponds to themaximum velocity, g_(n)(t) corresponds to the perceived gap, and T′corresponds to the specified time parameter.
 14. The system of claim 12,wherein the perceived gap is calculated using an equationx_(n-1)(t)−x_(n)(t)−s_(n-1), wherein x_(n-1)(t) corresponds to aposition of the leading vehicle, x_(n)(t) corresponds to a position ofthe following vehicle, and s_(n-1) corresponds to a length of theleading vehicle.
 15. The system of claim 12, wherein the processor isfurther configured to perform actions comprising: calculating a currentvelocity of the following vehicle at a current time; and selecting, asan output, a minimu of a set$\left\{ {\sqrt{\frac{{Vg}_{n}(t)}{T^{*}}},{{v_{n}(t)} + a},V} \right\},$wherein V corresponds to the maximum velocity, g_(n)(t) corresponds tothe perceived gap, T′ corresponds to the specified time parameter,v_(n)(t) corresponds to the current velocity, and a corresponds to amaximum allowable velocity change in a single time step.
 16. The systemof claim 15, wherein the processor is further configured to performactions comprising: providing the output to a user.
 17. The system ofclaim 12, wherein the processor is further configured to perform actionscomprising: identifying at least one additional vehicle in the trafficmodel ; repeating the identifying and the calculating for the at leastone additional vehicle; and generating a data set based on therepeating.
 18. The system of claim 12, wherein the processor is furtherconfigured to perform actions comprising: iterating a time step;repeating the identifying and the calculating according to the timestep; and generating a data set based on the repeating.
 19. The systemof claim 18, wherein the processor is further configured to performactions comprising: processing the data set to simulate a traffic flowwithin the traffic model.
 20. The system of claim 18, wherein theprocessor is further configured to perform actions comprising: storingthe data set in memory.
 21. The system of claim 12, wherein the leadingvehicle is stationary.
 22. The system of claim 12, wherein the trafficmodel is used to model a traffic flow in a transportationinfrastructure.